Adding Mixed Numbers
Adding mixed numbers requires adding the whole number parts and the fractional parts separately, finding a common denominator for the fractions first, then combining and simplifying. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students follow three steps: add the whole numbers, find the LCD and rename the fractions, add the fractions, then simplify. For 2 and 1/3 plus 1 and 1/2: LCD = 6; rename as 2 and 2/6 plus 1 and 3/6; add whole parts (3) and fraction parts (5/6) to get 3 and 5/6. If the fraction sum is improper, convert and add to the whole number total.
Key Concepts
Property Add the whole numbers together, then add the fractions separately. Find a common denominator for the fractions before you add them, then combine the whole and fractional parts and simplify.
Examples $$ 1\frac{1}{2} + 2\frac{1}{3} + 3\frac{1}{6} = (1+2+3) + (\frac{3}{6}+\frac{2}{6}+\frac{1}{6}) = 6 + \frac{6}{6} = 7 $$ $$ 1\frac{1}{4} + 1\frac{1}{8} + 1\frac{1}{2} = (1+1+1) + (\frac{2}{8}+\frac{1}{8}+\frac{4}{8}) = 3 + \frac{7}{8} = 3\frac{7}{8} $$ $$ 2\frac{1}{5} + 1\frac{1}{2} + \frac{3}{10} = (2+1) + (\frac{2}{10}+\frac{5}{10}+\frac{3}{10}) = 3 + \frac{10}{10} = 4 $$.
Explanation It’s a two step process! First, add the big numbers—the whole parts. Easy. Then, handle the smaller bits: the fractions. Find their common denominator, add them up, and join your two sums together. If the fractions make a new whole number, level up your whole number part. You're done!
Common Questions
What are the steps for adding mixed numbers?
1. Add the whole numbers. 2. Find the LCD and rename fractions with that denominator. 3. Add the fractions. 4. Combine with the whole number sum and simplify.
Add 2 and 1/3 plus 1 and 1/2.
LCD = 6. Rename: 2 and 2/6 + 1 and 3/6. Whole numbers: 2+1=3. Fractions: 2/6+3/6=5/6. Answer: 3 and 5/6.
Add 3 and 3/4 plus 2 and 1/2.
LCD = 4. Rename: 3 and 3/4 + 2 and 2/4. Whole: 5. Fractions: 3/4+2/4=5/4=1 and 1/4. Total: 5+1 and 1/4 = 6 and 1/4.
What do you do if the fraction sum is an improper fraction?
Convert the improper fraction to a mixed number and add its whole number part to the whole number sum. For example, if fractions sum to 5/4 = 1 and 1/4, add 1 to the whole number total.
Do you need a common denominator to add the whole number parts?
No. Add whole numbers directly. Only the fractional parts require a common denominator.